Calculation of the dielectric properties of a protein and its solvent: theory and a case study

This paper presents a rigorous derivation of a theory for the calculation of the frequency-dependent dielectric properties of each component of the system protein/water/ions with the aim of enabling comparison to experimentally determined dielectric properties. We apply this theory to a very long (13.1 ns) molecular dynamics simulation of an HIV1 zinc finger peptide, its co-ordinated zinc ion, and two chloride ions in a box of SPC/E water molecules. We find the dielectric relaxation of the water molecules restricted compared to pure water, giving rise to a static dielectric constant for the water-component of only 47. The peptide is found to have a complicated dielectric relaxation behaviour, with a static dielectric constant of 15. We also calculate the frequency-dependent conductivity of the ions in this system. We analyze all contributions to the calculation of these dielectric properties and find that the coupling between the dielectric relaxation of the peptide and that of the water-component is particularly important for correctly describing the dielectric constant of the peptide.